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With a sufficiently fine discretisation, the Lattice Boltzmann Method (LBM)mimics a second order Crank-Nicolson scheme for certain types of balance laws(Farag et al. [2021]). This allows the explicit, highly parallelisable LBM toefficiently solve the fundamental equations of solid mechanics: theconservation of mass, the balance of linear momentum, and constitutiverelations.  To date, all LBM algorithms for solid simulation - see e.g. Murthy et al.[2017], Escande et al. [2020], Schl\"uter et al. [2021] - have been limited tothe small strain case. Furthermore, the typical interpretation of the LBM inthe current (Eulerian) configuration is not easily extensible to large strains,as large topological changes complicate the treatment of boundary conditions.  In this publication, we propose a large deformation Lattice Boltzmann Methodfor geometrically and constitutively nonlinear solid mechanics. To facilitateversatile boundary modelling, the algorithm is defined in the reference(Lagrangian) configuration.

A Lattice Boltzmann Method for nonlinear solid mechanics in the reference configuration